Power Functions Examples

Example 1

There's a skill needed for integrals that we'll consider now: thinking backwards. Instead of taking a function and figuring out its derivative, think about looking at a derivative and figuring out what sort of function it came from. Try this out when looking over solutions to derivatives.

If f'(x) = 5x4, what could the original function f(x) be?

The derivative

f'(x) = 5x4 = 5x5–1

looks like it came from the rule for derivatives of power functions. The original exponent must have been 5, therefore the original function could have been